Drogba says sorry for lobbing coin at fans
"We are investigating the incident as a whole," a police spokesman said on Thursday. "It's obviously very early stages at the moment."
Drogba had gestured to Burnley fans while celebrating his first goal of the season. Championship Burnley won 5-4 on penalties after the fourth round tie ended 1-1 following extra time.
"I tried to celebrate the goal and I received some things at me," he told the Chelsea website.
"The big mistake I did was to throw it back so if someone was hurt I just want to apologise for it. This is not something I should show in a football match.
"It was an incident in the heat of the moment and I regret it. It was just a mistake and nothing more."
An FA spokesman said the governing body would issue a statement later on Thursday.